" According to Bell's theorem, the degree of correlation between spatially separated measurements on a quantum system is limited by certain inequalities if one assumes the condition of locality. Quantum mechanics predicts that this limit can be exceeded, making it nonlocal. We analyse the effect of an environment modelled by a fluctuating magnetic field on the quantum correlations in an EPR singlet as seen in the Bell inequality. We show that in an EPR setup, the system goes from the usual 'violation' of Bell inequality to a 'non-violation' for times larger than a characteristic time scale which is related to the parameters of the fluctuating field. We also look at these inequalities as a function of the spatial separation between the EPR pair. "
source: https://arxiv.org/pdf/quant-ph/9501021.pdf
Article Effect of Decoherence on Bell's Inequality for an EPR Pair
The experiment assumes that the two photons will have the exact same polarization. Even if this experiment is done under a man made vacuum which is not perfect and EM shielded from environment, nothing ensures that the two photons will have the exact same polarization just before they hit the polarizers. You can not isolate completely the environment. Therefore the probability will be always less than 1/3 due quantum decoherence. To say that because by proof of contradiction one theory of the two is the correct is far fetched and proves neither of the two just that this is not a control experiment. σ figure does not matter if this is not a control experiment.
Here is another voice of concern:
Article Experimental Non-Violation of the Bell Inequality
Emmanouil Markoulakis
Research Fellow
HMU 2020